Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #6 Dec 20 2022 19:19:16
%S 67,17317,80317,97117,398467,1333417,1423717,1876267,2317267,3332167,
%T 4890367,5456317,5911417,6151867,6622867,9151717,9522367,11013967,
%U 13372717,15381967,17080267,21663067,22439017,22552417,24262267
%N Primes of form: sum of prime 5-tuples (A022007).
%F 7+11+13+17+19=67
%t lst={};Do[p=Prime[n];If[PrimeQ[p+4]&&PrimeQ[p+6]&&PrimeQ[p+10]&&PrimeQ[p+12],s=p+p+4+p+6+p+10+p+12;If[PrimeQ[s],AppendTo[lst,s]]],{n,10!}];lst
%t Select[Total/@Select[Partition[Prime[Range[350000]],5,1],Differences[#]=={4,2,4,2}&],PrimeQ] (* _Harvey P. Dale_, Dec 20 2022 *)
%K nonn
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, Sep 25 2008